Dividing decimals; fractions to decimals worksheet

Part A: Working out and filling in

1. 1. 562 ÷ 100 = 5.62

   562 ÷ 100: 562 is whole, so its point sits at the end; ÷100 moves the point two places left, 562 ÷ 100 = 5.62

2. 2. 1.12 ÷ 10 = 0.112

   1.12 ÷ 10: ÷10 moves the point one place left, filling in zeros at the front, 1.12 ÷ 10 = 0.112

3. 3. 22.4 ÷ 0.8 = 28

   22.4 ÷ 0.8: move both points one place right to make the divisor whole: 224 ÷ 8 = 28

4. 4. 8.2 ÷ 2 = 4.1

   8.2 ÷ 2: divide as whole numbers, 82 ÷ 2 = 41, then put the point back one place → 4.1

5. 5. 11.4

   Multiply before adding: work out 1.4 × 7 first, then add 1.6.

   Multiply first: 1.4 × 7 = 9.8, then 1.6 + 9.8 = 11.4.

6. 6. 59

   The divisor is a decimal, so multiply both by 10: 178 ÷ 3. Then divide to the first decimal place.

   Make the divisor whole: 178 ÷ 3; divide to the first decimal place, then round to a whole number: 59.

7. 7. 1.93

   For 2 decimal places, divide 5.8 ÷ 3 to the third place, then look at that digit.

   Divide to the third decimal place, then round to the second: 1.93.

8. 8. 310 = 0.3

   310: the denominator is 10 already, 3 ÷ 10 = 0.3

9. 9. 14 = 0.25

   14: scale it to a denominator of 100, multiplying the numerator and denominator by 25: 1 × 25 = 25, 4 × 25 = 100 → 25100 = 0.25

Part B: Choose, or true or false

1. 10. C. 3.1 ÷ 0.4

   There are no brackets, so look for a × or ÷ sign first.

   × and ÷ come before + and −: the only division is 3.1 ÷ 0.4, so it comes first.

2. 11. False

   Turn 725 into a decimal first: 7 ÷ 25. Then compare it with 0.3 place by place.

   725 = 7 ÷ 25 = 0.28; then compare it with 0.3 place by place.

3. 12. B. 89

   Turn each fraction into a decimal (numerator ÷ denominator) and see which lands between 0.8 and 0.9.

   89 = 8 ÷ 9, which is between 0.8 and 0.9.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 1000 grains of rice weigh 19 g altogether. On average, how many grams does each grain weigh? (Answer: 0.019 g)

   19 ÷ 1000 = 0.019

2. 14. Ka-yan bought 5 identical highlighters for $39.5 altogether. How many dollars did each highlighter cost? (Answer: 7.9 dollars)

   39.5 ÷ 5 = 7.9

3. 15. 4.7 dollars

   Find what each kind costs first, 3 × 13.5 and 3 × 1.6, then add them.

   May paid $50, so the change is 50 minus the total.

   3 × 13.5 = 40.5 and 3 × 1.6 = 4.8, 45.3 in all; 50 − 45.3 = 4.7.

4. 16. 10 bows

   Work out 6.5 ÷ 0.6. Ribbon left over that won't make a whole bow doesn't count.

   6.5 ÷ 0.6 is a little more than 10; what's left isn't enough for another, so 10.

5. 17. A bottle holds 0.92 L of soy sauce. Written as a fraction in simplest form, how many litres is that? (Answer: 2325 L)

6. 18. 0.25 L

   Turn 1120 into a decimal first, 11 ÷ 20, then compare with 0.8 to see who had more.

   1120 = 0.55; compare with 0.8 and take the smaller from the bigger: 0.25 L.