Decimals And Ratio Worksheet Page 4
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13Check
Strengthen
Extend
Test
MASTER
P149
P151
P155
P159
6.3
Worked example
Calculations with decimals
Work out 67.8 ÷ 1.2
Key point
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____
1.2 has one decimal place, so
)
)
)
1.2
67.8
To divide by a decimal, multiply
×10
×10
You will learn to:
____
____
multiply both numbers by 10.
both numbers by a power of 10
)
)
)
12
678
•
Add and subtract decimals of any size
(10, 100, …) until you have a whole
5 6. 5
number to divide by.
•
Multiply and divide by decimals
___
___
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___
_
Work out the division.
)
)
)
12
6 7
7
8.
6
0
Then work out the division.
•
Divide by 0.1 and 0.01
Check: 12 × 56.5 ≈ 10 × 60 = 600
Fluency
6 Work these out using a written method.
Work out
Give your answers to one decimal place where appropriate.
•
57 – 14 – 23
Q6f hint
•
63 – 12 − 31
a 18.9 ÷ 0.09
b 39 ÷ 0.75
c 131.72 ÷ 0.37
Explore
You will need to work out the second
d 348 ÷ 5.8
e 43.32 ÷ 0.3
f 82.3 ÷ 6.25
Why does a sharp axe cut better
decimal place and then round, rather
Why learn this?
than a blunt one? Think about the
g 367 ÷ 2.4
h 0.556 ÷ 3.6
i 72.5 ÷ 0.7
than just stopping at the fi rst decimal
We need to calculate using decimals when dealing
area of the cutting surface.
place.
Discussion
‘Dividing a number by a number less than 1 gives you an
with money and measurements.
answer larger than the fi rst number.’ Is this statement true?
7
STEM
A scientist has 27.9 g of substance X.
Exercise 6.3
He needs to divide it into samples for testing.
Each testing dish holds 2.4 g.
1
Finance
Billy has been checking his bank statement.
How many testing dishes does the scientist need?
Date
Paid in
Paid out
Balance
8 Work out
16/09/2013
Start balance
£125.68
Q8a hint
a 3241 + 306.192 + 2.308
b 806.5 – 21.33 − 95
Water bill
£23.75
Keep the decimal points in line.
Electricity
£17.29
c 3150.14 – 88.6 + 27.2031
d 3096 + 108.7 + 0.204 – 3.14
3241
Lotto
£10.00
306.192
Mobile
£15.99
9
STEM / Problem-solving
Suzie is testing a beaker of water.
+
2.308
Q1 Literacy hint
Wages
£256.75
She removes these samples for analysis.
Your bank balance is the amount of
17/09/2013
End balance
A
B
C
D
money in your account.
2.13 ml
0.005 ml
3.075 ml
0.321 ml
What is the balance of Billy’s account after his wages are paid in?
a There is 32.4 m l in the beaker after samples A and B are removed.
l in the beaker after samples A and B are removed.
l
How much water was originally in the beaker?
2 Work out
a 4.83 × 2.7
b 2.45 × 3.32
b How much water is left in the beaker after all samples are removed?
3 Use a written method to calculate
10
Real / Problem-solving
A skateboard factory makes boards from
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____
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____
)
)
)
)
)
)
a 3
b 23
sheets of plywood. The factory checks the area of plywood wasted
294
943
each week. One week the total waste was 28.75 m
2
over the fi ve days
4 Work out
the factory was open.
a 36 ÷ 12 and 3.6 ÷ 1.2
b 72 ÷ 8 and 7.2 ÷ 0.8
Day
Waste
c 484 ÷ 4 and 4.84 ÷ 0.04
d 625 ÷ 25 and 6.25 ÷ 0.25
Monday
4.35 m
2
Discussion
What do you notice? How does this help you work out
Wednesday
5.4 m
2
8.1 ÷ 0.9 and 0.64 ÷ 0.08 without a calculator?
Thursday
6.14 m
2
5 Work out
a How much plywood was wasted on Tuesday and Friday?
a 6.3 ÷ 0.7
b 4.8 ÷ 0.6
c 12.1 ÷ 1.1
On Friday 2.4 m
2
more plywood was wasted than on Tuesday.
d 0.28 ÷ 0.07
e 0.9 ÷ 0.03
f 14.4 ÷ 0.12
b How much was wasted on Tuesday?
Topic links : Written multiplication and division, Metric measures,
Subject links : Science (Q7, Q9)
141
Unit 6
Decimals and ratio
142
Volume
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