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time yourself

Maths B (practice)Fri 9 October1 / 4

Dividing by a decimal, in words

Diagram first, then the calculation. An answer with no diagram is not marked right

Name Date

Today's four tools (last week continued)

① Make the divisor whole　multiply both numbers by the same thing.
② Keep dividing　if it does not come out even, put 0s after the remainder and continue.
③ Remainder　its decimal point lines up with the point in the original number.
④ "□ times" problems　first decide in a diagram which quantity is "1".

Before any calculating, this diagram. Top and bottom move in step. Whether the ? sits to the right or left of 90 tells you in advance if the answer is bigger or smaller.

Worked example

0.6 kg of beans cost 90 yen. What does 1 kg cost?
① Diagram (above). 1 kg is more than 0.6 kg → the answer must be more than 90
② Calculation　90 ÷ 0.6　　③ Both times 10　900 ÷ 6 = 150
④ Check　150 × 0.6 = 90 ✓　　Answer 150 yen

1 · Estimate first, then calculate

1Answer without calculating. For which □ is 9 ÷ □ bigger than 9? Choose all of them.
　A 0.8　　B 1.5　　C 0.09　　D 1.01

time yourself

Maths B (practice)Fri 9 October2 / 4

Dividing by a decimal, in words

Name Date

First, the most common mistake

"8.9 ÷ 0.4 = 22 remainder 1"　The decimal point in the remainder has been forgotten.
89 ÷ 4 = 22 remainder 1. But the remainder lines up with the point in the original 8.9, so it is 22 remainder 0.1 (0.4 × 22 + 0.1 = 8.9). With "remainder 1" the check would give 9.8, not 8.9.

2Find 7.8 ÷ 0.65.

Multiply both by what to make the divisor whole?

3Find 4.2 ÷ 0.8, continuing until it comes out exactly.

Put a 0 after the remainder of 42 ÷ 8 and carry on.

4Find 9.5 ÷ 0.6, rounding the quotient to one decimal place.

Work to two decimal places, then round.

5Find 8.9 ÷ 0.4 with a whole-number quotient, and write the remainder. Write the check too.

time yourself

Maths B (practice)Fri 9 October3 / 4

Dividing by a decimal, in words

Name Date

2 · "Times" and "per one" word problems

6B weighs 3.84 kg, which is 1.6 times A. How much does A weigh? Draw a diagram (a bar or a double number line) before the calculation.

With A as 1, B is 1.6.

72.4 kg of fertiliser covers a field of 3.6 m².
　(1) How many m² does 1 kg cover?
　(2) How many kg are used on 1 m²? Round to two decimal places.
Draw the double number line first.

In (1) and (2), the thing that becomes "1" is different.

8Tea, 3.2 L, is poured into bottles of 0.35 L each. How many bottles, and how many litres of tea are left over? Draw it.

time yourself

Maths B (practice)Fri 9 October4 / 4

Dividing by a decimal, in words

Name Date

9This year's yuzu weighed 5.5 kg, which is 1.25 times last year's. How many kg was it last year? Draw it.

10A rectangle has an area of 8.64 cm². It is 2.4 cm wide. How many cm tall is it? Draw it.

11A car goes 12.5 km on 1 L. How many litres does it need for 7.5 km? First say whether the answer is more or less than 1 L.

12Write only the calculation. Decide between × and ÷ with a double number line.
　(1) String costs 120 yen a metre. What do 2.5 m cost?
　(2) String costs 120 yen for 2.5 m. What does 1 m cost?

Same numbers, but what counts as "1" changes the calculation.