1 Find the totals of these decimals. a) 0.4 + 0.5 =
b) 0.7 + 0.1 + 0.1 =
c) 0.3 + 0.1 + 0.3 = d) 0.5 + 0.5 =
2 Max cuts some pieces of string. He measures the lengths.
a) How much longer is A than B? – =
b) What is the difference between A and C? – =
Adding and subtracting decimals
1
3 Complete the part-whole models.
4 Complete the calculations.
a) 0.3 + 0.5 = f) 0.7 – = 0.2
b) 0.7 + 0.1 = g) 0.4 + 0.3 + 0.2 =
c) 0.2 + = 0.5 h) 0.7 + 0.2 – 0.3 =
d) 0.5 – 0.1 = i) 0.9 – 0.1 + 0.2 =
e) 0.8 – 0.2 = j) 0.5 – 0.2 – 0.3 =
5 Complete the following calculations.
a) 0.3 + 0.7 = c) + 0.1 = 1 e) 1 – 0.5 =
b) 0.6 + = 1 d) 1 – 0.2 = f) 1 – = 0.2
6 Complete the addition pyramids. Each row of the pyramid must total the
same as the other rows.
a) b) c) d)
0.8
0.8
0.1
0.8
0.8
0.3 0.1 0.2 0.3 0.4 0.2 0.1 0.8 0.5 0.1 0.9 0.2 0.1Refl ect
Emma calculates 0.4 + 1 = 0.5. Explain the mistake Emma has made.
8 Write the numbers 0.1, 0.2, 0.3, 0.4, 0.5 and
0.6 in the circles so that the sum of each side of the triangle is equal to 0.9.
Use each number once.
7 If ◆ and ▲ are two decimal numbers less than 1 and ▲ – ◆ = 0.3,
what could ▲ and ◆ be?
▲ = ◆ = .
1 Mo adds different amounts of water and orange to make orange squash. Complete the additions.
a) 0.36 l + 0.22 l = l
b) 0.25 l + 0.47 l = l
c) 0.55 + 0.31 = d) 0.38 + 0.38 =
Adding and subtracting decimals
2
O • Tth Hth • 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 • 0.1 0.1 0.01 0.01 O • Tth Hth • 0.1 0.1 0.01 0.01 0.01 0.01 0.01 • 0.1 0.1 0.1 0.1 0.010.01 0.010.01 0.01 0.01 0.01 0.36 l 0.22 l Water Orange O . Tth Hth 0 . 3 6 + 0 . 2 2 . O . Tth Hth 0 . 2 5 + 0 . 4 7 . O . Tth Hth 0 . 5 5 + 0 . 3 1 . O . Tth Hth . + . .
2 Kate works out 0.05 + 0.12 as a column addition. Explain Kate’s mistake.
O . Tth Hth
0 . 5
+ 0 . 1
2
➜Textbook 5C p123 A running race is 0.65 km long. Lee runs 0.34 km. How far is left to run?
0.65 km – 0.34 km = km
4 Complete the subtractions.
a) 0.92 – 0.58 = c) 0.71 – 0.24 = b) 0.49 - 0.19 = d) 0.60 – 0.45 = O • Tth Hth • 0.1 0.1 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 O . Tth Hth 0 . 6 5 – 0 . 3 4 . O . Tth Hth 0 . 9 2 – 0 . 5 8 . O . Tth Hth 0 . 4 9 – 0 . 1 9 . O . Tth Hth 0 . 7 1 – 0 . 2 4 .
5 Complete the missing numbers in these models.
a) b) c) 0.28 0.09 0.34 0.66 0.35 0.67
Refl ect
Explain how Alex can use 37 + 59 to fi nd the sum of 0.37 and 0.59.
7 Use four different digits from 1, 2, 3, 4, 5, 6, 7, 8, 9 to:
a) Make the greatest total you can, less than 1.
b) Make the greatest difference you can, less than 1.
6 Ambika is using a number line to work out a calculation.
What two possible calculations might Ambika be working out?
0 . + 0 . 0 . 0 . – 0 . 0 . 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 + 0.05 + 0.52 0.15 0.72
1 Use the hundredths grids to help you fi nd the missing numbers.
a) 0.8 + = 1 b) 0.69 + = 1
2 Draw lines to match the pairs that make 1 m when added together.
You may not be able to fi nd a pair for all of the pieces.
Adding and subtracting decimals
3
3 Lexi has made a number on a place value grid.
What mistake has Lexi made?
What counters does she need to add?
4 a) Find the missing numbers.
i) ii) iii)
b) For part i) complete 4 number sentences.
0.38 + = 1 + = 1
1 – = – =
5 Complete the following.
a) 0.3 + = 1 d) 0.90 + = 1 g) 1 – 0.24 = b) 0.71 + = 1 e) + 0.787 = 1 h) 1 – = 0.07 c) + 0.05 = 1 f) 0.912 + = 1 i) 1 – 0.235 = O • Tth Hth • I need to add 0.84 to make 1. 0.38 1 0.384 1 0.380 1 Lexi 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01
Refl ect
Andy says, ‘0.207 + 0.793 = 1.’ Do you agree? Explain your answer.
6 Work out the missing numbers.
a) 0.4 + = 1 b) 0.4 + = 1
0.04 + = 1 0.40 + = 1
0.004 + = 1 0.400 + = 1
7 a) Use six digits from 1, 3, 4, 5, 7, 8 to make two decimal
numbers that add up to 1. You can use the same digit more than once but not within the same number.
O . Tth Hth Thth 0 .
+ 0 .
1 . 0 0 0
b) Find two different answers for part a ).
What is the same and what is different about your answers?
1 Complete these decimal additions. a) 0.37 + 0.82 =
b) 0.675 + 0.721 =
c) 0.56 + 0.78 = d) 0.7 + 0.7 = e) 0.82 + 0.78 =
Adding and subtracting decimals
4
O • Tth Hth • 0.1 0.1 0.1 0.010.01 0.010.01 0.01 0.01 0.01 • 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.01 0.01 O • Tth Hth Thth • • 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.001 0.001 0.001 0.001 0.001 0.001 0.01 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 O . Tth Hth 0 . 3 7 + 0 . 8 2 . O . Tth Hth 0 . 5 6 + 0 . 7 8 . O . Tth Hth 0 . 8 2 + 0 . 7 8 . O . Tth 0 . 7 + 0 . 7 . O . Tth Hth Thth 0 . 6 7 5 + 0 . 7 2 1 . ➜Textbook 5C p20
2 Match each calculation with its answer.
3 How much do the ruler and eraser cost altogether?
The ruler and eraser cost £ altogether.
4 Amal uses the treadmill at the gym.
He thinks he ran further on Thursday than he did from Monday to Wednesday in total. Is Amal correct?
Day Distance Monday 0.625 km Tuesday 0.193 km Wednesday 0.208 km Thursday 1.25 km 0.23 + 0.84 0.76 + 0.52 1 + 0.17 0.74 + 0.63 0.54 + 0.85 1.39 1.37 1.07 1.28 1.17 £0.89 £0.65
Refl ect
Jamie says, ‘0.5 + 0.6 = 0.11.’ Explain why Jamie is wrong.
6 Use the signs <, = or > to complete each statement.
Explain how you worked out your answers.
a) 0.51 + 0.63 0.51 + 0.73
b) 0.7 + 0.4 0.71 + 0.39
5 Write the missing numbers.
a) O . Tth Hth b) c) 0 . 4 3 + 0 . 7 . 1 O . Tth Hth 0 . + . 5 9 1 . 3 7 O . Tth Hth Thth 0 . 7 3 2 + 0 . 7 . 1 3
1 There are some books for sale in a charity book shop.
a) How much do the Dictionary and Animals of the World cost altogether?
The total cost is £ .
b) Work out the cost of Learn Spanish and Jed’s Diary.
The total cost is £ .
Adding and subtracting decimals
5
O . Tth Hth 6 . 5 0 + 4 . 3 1 . O . Tth Hth 5 . 7 6 + 3 . 7 9 . Jed’s Diary Animals of the World Dictionary Learn Spanish £3.79 £6.50 £5.76 £4.31 O • Tth Hth • • 1 1 1 1 1 1 1 1 1 1 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 O • Tth Hth • • 1 1 1 1 1 1 1 1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
2 Complete the additions.
3 Work out the totals and use the >, < or = sign to complete each number sentence.
a) 0.502 + 4.165 3.258 + 0.875 b) 8.62 + 6.18 2.63 + 1.71 + 3.26
4 Zac wants to buy
the scarf and the magazine.
He adds the amounts.
What mistake has Zac made? What is the correct answer?
T O · Tth Hth
1
1 . 2
3 . 6
9
4 . 8
1
1
5 Find the answers. Mark them on the correct place on the number line.
4.5 + 2.8 = 2.75 + 4.82 = 1.823 + 6.077 =
8.0
7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9
£3.69 £11.20
Refl ect
Explain how to add 4.53 and 3.78.
6 Reena’s dad wants to take Reena and her little sister
somewhere for her birthday. He has £50. Which activities can they afford to do?
Theatre Cinema Zoo Circus
Adult £29.50 £15.69 £19.90 £16.60
Child £9.75 £5.32 £12.50 £8.80
1 Danny buys a bottle of milk and loaf of bread.
The milk costs £1.05. The total cost of his items is £2.54 a) How much did the loaf of bread cost?
The loaf of bread costs £ .
b) Danny gives the shop keeper £2.70.
How much change does he get?
Danny gets £ change.
2 Complete the subtractions.
a) 5.4 – 3.2 = b) 7.26 – 4.83 = c) 2.661 – 0.625 =
Adding and subtracting decimals
6
O • Tth Hth 1 1 • 0.1 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 O . Tth Hth 2 . 5 4 – 1 . 0 5 . O . Tth Hth . – . . O . Tth 5 . 4 – 3 . 2 . ➜Textbook 5C p28
3 Complete the subtractions. a) 7.56 – 0.49 = b) 12.52 – 3.92 = O . Tth Hth 6 . 2 0 – 0 . 5 9 5 . 7 9 5 1
5 Holly is walking 24.5 km for charity. By 3 pm she has walked 18.7 km.
How much farther does Holly have to walk?
Holly has km left to walk.
4 Kate has £6.20 in her pocket. She buys a bottle of water for 59p.
Kate does this calculation to work out her change. What mistake has she made?
Refl ect
What is the same and what is different about these calculations? Explain how you would work out the answer to each one. a) 5.8 – 3.2 b) 5.8 – 3.9
7 How much greater is the difference between A and C than
the difference between B and C?
The difference between A and C is greater than
between B and C.
6 Complete the additions.
a) 3.21 + = 5.49 b) 12.99 = + 5.32 + 2.69 100 0 A 11.58 B 68.65 C 81.96
1 Bella fl ies a paper plane 2.31 m. Ebo’s paper plane fl ies 0.7 m. How much further did Bella’s paper plane fl y?
Bella’s plane fl ew m further than Ebo’s plane.
Adding and subtracting decimals
7
O . Tth Hth 2 . 3 1 – 0 . 7 0 . O . Tth Hth 3 . 6 2 – 4 . 8 . O . Tth Hth Thth 1 . 9 6 – 1 . 2 5 8 .
2 Work out the following calculations.
a) 3.62 + 4.8 = b) 1.96 – 1.258 =
3 Complete the calculations.
a) 4.7 + 33.64 = b) 9.5 + 1.872
6 Is Danny’s statement true?
Answer always, sometimes or never.
Give some examples to support your answer.
4 a) 16.9 – 11.87 = b) 118.7 – 3.95 =
T O . Tth Hth
5
3 . 4 9
–
3 .
7
5 0 . 4 2
Subtracting a number with 2 decimal places from a number with 1 decimal place will give an answer with 2 decimal places.
Danny
5 Zac is working out 53.49 – 3.7. Can you explain
the mistake in his calculation? What is the correct answer?
53.49 – 3.7 =
Refl ect
What are the most important things to remember when adding or subtracting decimals with a different number of decimal places?
8 These two cards have a difference of 1.55. What could the
sum of the two cards be?
How many answers can you fi nd?
7 Compare the number lines and fi nd the difference between A and B.
4.1 A 4.2 B 15 16
19.7
The difference between A and B is .
1 Ebo is working out 6 + 1.37. He makes both numbers using place value counters and then adds the numbers.
a) What answer did Ebo get?
b) Explain a different way Ebo could fi nd the answer.
2 All these calculations have the same answer. Find the missing numbers.
12 + 2.72 = 5 + .72 =
3 + 11. = 0.72 + =
5 + 5 + = 14.7 + =
3 Complete the column subtractions.
a) 7 – 3.8 = b) 12 – 4.35 =
Adding and subtracting decimals
8
T O . Tth Hth 1 2 . 0 0 – 4 . 3 5 . O . Tth Hth 6 . 0 0 + 1 . 3 7 . O . Tth 7 . 0 – 3 . 8 . O • Tth Hth • • 1 1 1 1 1 1 1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 0.1 0.1 ➜Textbook 5C p36
Suncream
300 ml
4 Bella works out 5 – 2.84 by doing 4.99 – 2.83.
Use Bella’s method to answer these calculations.
a) 8 – 2.807= b) 12 – 4.91 = c) 16 – 1.8 =
5 a) What is the total cost of these items?
The total cost is £
b) Mary uses 18.7 ml of sun cream.
How much is left?
There is ml of sun cream left.
6 Work out the following calculations.
a) 3 + 0.45 = d) 2 + 9 + 3.4 =
b) 17 + 8.725 = e) 380 m + 70.85 m = m
c) 3.67 kg + 7 kg = kg f) 28.513 + 48 + 399 =
£8 £5 £3.92
Refl ect
How can you use a number line to show that 7 – 2.4 is the same as 6.9 – 2.3?
8 Work out the missing numbers.
a) 8 – 3.92 = 4 + b) 7.9 – 5.42 = 12 –
7 How much more milk than lemonade is there?
There is ml more milk than lemonade. 6 litres
1 litre 1.75 litre
4 litres
2 litres
1 Work out the missing numbers in each sequence.
a) 4.6, 4.7, 4.8, , , ,
b) 11.5, 11.9, , 12.7, , 13.5, ,
c) , , 15.65, 15.6, 15.55, ,
2 Complete the numbers on the number line.
a)
b)
3 Kate is counting up by the same amount each time.
Decimal sequences
0, 0.3, 0.6, 0.9, 0.12, 0.15
0.76 0.77
5.615 5.620 5.630 5.645
Kate
What mistake has Kate made?
4 Complete the sequence and write whether each rule is true or false.
a) 10.1, 10.3, 10.5, 10.7, c) 3.0, 2.25, 1.5, 0.75,
The rule is ‘add 0.2’. The rule is ‘subtract 0.25’.
b) 39.57, 39.60, 39.63, 39.66, d) 0.4, 0.52, 0.64, 0.76,
The rule is ‘add 0.3’. The rule is ‘add 0.12’.
5 Max is counting up by 0.02 each time. He starts at 12.45.
a) What are the next three numbers Max will say?
The next three numbers Max will say are , , .
b) Max stopped when he reached the fi rst number above 18.
What number did Max stop on?
6 Complete the sequences. Write the rule for each sequence.
a) 0.21, 0.42, 0.63, , 1.05, 1.26, b) 11.3, , 12.1, , , 13.3, 13.7 c) 7.68, 7.61, 7.54, 7.47, , , 7.26 Rules: a) b) c) Max 12.45, 12.47 …
Refl ect
Make a sequence using decimal numbers. Ask a partner to continue the sequence. What rule did you use?
7 Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. In round 2, he then runs from A to C and back to A.
He continues in the same pattern until round 6, when he runs A to G and back to A.
Complete the table to show how far Toshi runs each round and in total.
Round 1 2 3 4 5 6 Distance travelled in round (km) Total distance travelled so far (km)
7 Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. Seven cones are spaced equally apart for a running race.
In round 1, Toshi starts at A, runs to B and then back to A. A B C D E F G 0.4 km 0.4 km 0.4 km 0.4 km 0.4 km 0.4 km
1 Work out the missing values on the bar models. a)
b)
c)
Problem solving – decimals
1
54.47 kg 44.305 kg 80.36 m 24.98 m £ £12.67 £15.03 £28.98 kg m ➜Textbook 5C p44
Refl ect
2 Toshi drives 26.3 km to work. He then drives 6.85 km to his gran’s house.
How far does he drive in total?
Toshi drives km in total.
3 What is the mass of the grape?
The mass of the grape is g.
4 Circle the two numbers that add up to 1.2 but have a difference of 0.78.
18.4 g 20.95 g
1.12
0.8
0.12
0.21
0.90
0.99
Refl ect
Look at the bar models in question 1. Write a question that you could solve using one of the bar models.
6 Isla has £20. She spends £3.20 on a magazine. She then
buys a book that costs £5.90 more than the magazine. How much change should Isla receive in total?
5 Complete the calculation.
100 – 1.0 – 0.1 – 0.01 – 0.001 =
1 Amelia buys three items.
How much do the three items cost in total?
The total cost of the three items is £ .
2 Danny buys two items for his dog. He buys a chew toy costing £4.67 and
a lead that costs £2.85 more than the chew toy. He pays with a £20 note. How much change does Danny get?
£12.50
Problem solving – decimals
2
£12.50 £4.79 £0.75
?
£0.75 £4.79
3 A bucket has 8.751 l of water in it. Amal pours a further 7.5 l into the bucket. 1.27 l of water spill out because the bucket is full.
How much water does the bucket hold?
4 Choose three numbers from the cards that make the calculation true.
+ – = 10
5 Three identical rectangles are put together with their edges touching.
What is the length of the side marked A?
0.345
2.233
3.578
8.655
12.178
2.65 m
1.9 m A
Refl ect
Write a problem-solving question with the answer 3.21 kg. Ask your partner to check the answer.
7 Kate and Richard have both saved some money.
Richard needs to save another £1.20 to make £100.
After paying £24.78 for stationery, Kate has £36.98 less than Richard. How much more money has Richard saved than Kate?
6 When added together, these two cards total 9.2.
What is the difference between the cards?
4.59
1 Use the place value grids to help you complete these multiplications.
a) 2.4 × 10 = b) 0.13 × 10 =
2 Complete the multiplications.
a) 1.3 × 10 = c) 13.5 × 10 = b) 1.35 × 10 = d) 0.135 × 10 =
Multiplying decimals by 10
T O • Tth 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 O • Tth Hth • 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 H T O • Tth Hth Thth 1 • 3 • H T O • Tth Hth Thth 1 • 3 5 • H T O • Tth Hth Thth 0 • 1 3 5 • H T O • Tth Hth Thth 1 3 • 5 • ➜Textbook 5C p523 Olivia says, ‘14.8 × 10 = 14.80.’ What mistake has Olivia made? What is the correct answer?
4 Draw lines to match each multiplication to its answer.
5 Complete the multiplications.
0.003 × 10 3.53 × 10 0.03 × 10 10 × 0.353 0.3 × 10 10 × 3.003 0.0353 × 10 0.03 3 35.3 30.03 0.353 0.3 3.53 a) 5.8 × 10 = h) 0.019 × 10 = b) 5.82 × 10 = i) = 3.09 × 10 c) 24.9 × 10 = j) 0.04 × 10 = d) 1.09 × 10 = k) = 3.099 × 10 e) 21.08 × 10 = l) 0.004 × 10 = f) 0.198 × 10 = m) = 30.99 × 10 g) 10 × 21.08 = n) 0.040 × 10 =
Refl ect
Explain what happens to the digits when you multiply a decimal number by 10.
7 Mo’s stride is 0.8 metres long. Lexi’s stride is 0.65 metres long.
They each take 20 strides.
How much further has Mo travelled than Lexi?
Mo has travelled m further than Lexi.
6 a) Luis is working out the missing number in × 10 = 12.5.
He thinks the missing number is 125. Is Luis correct? Explain your answer.
b) Work out the missing numbers.
× 10 = 15 × 10 = 9.2 × 10 = 1.73
× 10 = 25 10 × = 15.2 × 10 = 17.3
1 Complete the place value grids to work out the answers. a) 7.9 × 10 = 7.9 × 100 = 7.9 × 1,000 = b) 2.19 × 10 = 2.19 × 100 = 2.19 × 1,000 = c) 0.84 × 100 = e) 0.05 × 100 = d) 0.7 × 1,000 = f) 1,000 × 1.7
Multiplying decimals by 10, 100 and 1,000
2 Complete the calculations. a) 0.4 × 100 = c) × 100 = 912 0.04 × 100 = × 100 = 91.2 0.004 × 100 = × 1,000 = 9.12 100 × 0.4 = 1,000 × = 91.2 b) 1.7 × 100 = d) 4.5 × = 450 1.7 × 1,000 = 0.045 × = 4.5 0.17 × 1,000 = 0.045 × = 0.45 0.045 × = 45
3 a) Sofi a buys 1,000 cans of orange juice for the school café. One can
contains 0.335 litres of juice.
How many litres of orange juice did Sofi a buy?
b) The length of a blue straw is 0.11 m. The length of a red straw is 0.09 m.
What is the total length of 100 blue and 100 red straws?
5 Use the number cards to fi nd three ways to complete each calculation.
a) × = 68 b) × = ×
× = 68 × = ×
× = 68 × = ×
4 Complete the missing numbers in this multiplication grid.
Number 0.38 0.012
× 3.6 380 76.91
× 12.07 1.2
10
100
1,000
6.8
0.68
0.068
Refl ect
Complete the sentences:
• Multiplying by 100 is the same as multiplying by and again.
• Multiplying by 1,000 is the same as multiplying by and
and again.
Show your partner how you can use a place value grid to multiply by 100 or 1,000.
1 Use the place value grids to help you work out the divisions. 1.2 ÷ 10 =
Dividing decimals by 10
O • Tth Hth 1 • 0.1 0.1 O • Tth Hth • 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 T O • Tth Hth 1 • 2 • Th H T O • Tth Hth 4 • 5 • Th H T O • Tth Hth 4 5 • • Th H T O • Tth Hth • • Th H T O • Tth Hth • •2 Work out these divisions.
a) 4.5 ÷ 10 = c) 45 ÷ 10 =
b) 0.45 ÷ 10 = d) 4.52 ÷ 10 =
➜Textbook 5C p60
3 What number should go in each part of the bar?
÷ =
4 10 apples have a total mass of 2.8 kg. Each of the apples has the same mass.
What is the mass of one apple?
The mass of one apple is kg.
5 Work out the following missing numbers.
a) 603 ÷ 10 = d) 75.3 ÷ = 7.53 g) 0.035 = ÷ 10
b) 160.3 ÷ 10 = e) ÷ 10 = 0.08 h) 8.719 = ÷ 10
c) 16.31 ÷ 10 = f) 3.978 ÷ 10 = i) 3.895 × 10 = ÷ 10
6 Is Max correct? Explain any mistakes.
? ? ? ? ? ? ? ? ? ? 2.31 Max 10 books costs £35, so each book costs £3.5.
Explain how to divide a decimal number by 10. Explain how to divide a decimal number by 10. Explain how to divide a decimal number by 10. Explain how to divide a decimal number by 10.
Refl ect
8 Toshi has 2.5 kg of hot chocolate powder. He makes 10 cups
of hot chocolate every week for 10 weeks before it runs out. How much does he use in each cup? Give your answer in kg.
Toshi uses kg of hot chocolate powder in each cup.
7 a) What is the cost of 100 ml of lemonade?
100 ml of lemonade costs £ .
b) What is the cost of 200 g of cocoa? Explain your answer.
200 g of cocoa costs £ .
1 l
1 kg £1.80 £121 Use the place value grids to answer these questions.
a) 23 ÷ 100 = c) 5.2 ÷ 100 =
b) 145 ÷ 1,000 = d) 13 ÷ 1,000 =
2 Use the tenths grid to show if Bella is correct.
Explain your answer.
Dividing decimals by 10, 100 and 1,000
3 Write true or false under each calculation. Correct those that are incorrect. a) 9 ÷ 100 = 0.09 c) 53 ÷ 100 = 0.053 e) 8.7 ÷ 100 = 0.87 b) 7 ÷ 1,000 = 0.007 d) 75 ÷ 1,000 = 0.075 f) 9.1 ÷ 1,000 = 0.00091 0.8 ÷ 100 0.18 ÷ 100 10.8 ÷ 100 0.108 ÷ 10 108 ÷ 1,000 0.08 ÷ 100 8 ÷ 1,000 1.8 ÷ 1,000 1.08 ÷ 100
5 Complete the calculations.
a) 3.7 ÷ = 0.37 b) ÷ 10 = 0.12
3.7 ÷ = 0.037 ÷ 100 = 0.12
3.7 ÷ = 0.0037 ÷ 1,000 = 0.12
4 Draw lines to match the calculations that give the same answer. Not all
have a pair.
My journal
Refl ect
Reena thinks that 0.351 ÷ 10 = 3.51 ÷ 100 and 3.51 ÷ 100 = 35.1 ÷ 1,000. Is Reena correct? Explain your answer.
7 Each shape represents a different number. Find the
missing values.
■ ÷ 10 = ▲ × 100 = 0.098 ★ × 10 = 0.61 ÷ 100 = ●
■ = ★ =
▲ = ● =
6 Each day Zac and Jamie put some
money in their money box.
After 100 days Zac has £18 and Jamie has £124.
If they always put in the same amount each day, how much more money did Jamie save each day in pounds?
Jamie saved £ more each day.
End of unit check
My journal
1 Max is working out 12 – 4.35.
a) Show two different ways Max could do this.
What advice would you give Max?
b) What mistakes should Max be careful not to make when subtracting decimals?
➜Textbook 5C p68
Power check
How do you feel about your work in this unit?
2 What is the same and what is different about these calculations?
Power play
The aim is to fi nd a path from 2 to 0.002.
How many different paths can you fi nd? Use the place value grid to help you.
Now fi nd a route where the answer is 2!
TTh Th H T O • Tth Hth Thth • • 2 ÷ 100 ÷ 10 × 100 × 10 ÷ 100 ÷ 1,000 × 100 × 10 ÷ 10 × 100 × 10 × 10 ÷ 100 × 10 ÷ 10 × 100 ÷ 1,000 × 100 ÷ 10 × 1,000 × 100 × 10 2 2 ÷ 100 ÷ 10 × 100 × 10 ÷ 100 ÷ 1,000 × 100 × 10 ÷ 10 × 100 × 10 × 10 ÷ 100 × 10 ÷ 10 × 100 ÷ 1,000 × 100 ÷ 10 × 1,000 × 100 × 10 0.002
Explain your method.
