Mixed operations with decimals worksheet

Part A: Working out and filling in

1. 1. 8.4

   Brackets come first: find 43.7 − 1.7, then divide by 5.

   Brackets first: 43.7 − 1.7 = 42, then 42 ÷ 5 = 8.4.

2. 2. 2.6

   Multiply before adding: work out 0.3 × 3 first, then add 1.7.

   Multiply first: 0.3 × 3 = 0.9, then 1.7 + 0.9 = 2.6.

3. 3. 8.8

   Multiply before adding: work out 0.7 × 7 first, then add 3.9.

   Multiply first: 0.7 × 7 = 4.9, then 3.9 + 4.9 = 8.8.

4. 4. 7.8

   The subtraction waits: work out 4.8 ÷ 0.4 and 0.6 × 7 on their own first, then subtract.

   Divide and multiply first: 4.8 ÷ 0.4 = 12 and 0.6 × 7 = 4.2; then 12 − 4.2 = 7.8.

5. 5. 3

   The subtraction waits: work out 2.5 ÷ 0.5 and 1 × 2 on their own first, then subtract.

   Divide and multiply first: 2.5 ÷ 0.5 = 5 and 1 × 2 = 2; then 5 − 2 = 3.

6. 6. 36

   Both parts multiply 3.6, so add 5.5 and 4.5 first and see what you get.

   Both parts multiply 3.6, so join them: 3.6 × (5.5 + 4.5) = 3.6 × 10 = 36.

7. 7. 6.7

   You can multiply in any order. 0.25 × 4 is a friendly pair, so do that first.

   Multiplying can be done in any order: 0.25 × 4 = 1 first, then times 6.7: 6.7.

8. 8. 36

   Both parts multiply 3.6, so add 2 and 8 first and see what you get.

   Both parts multiply 3.6, so join them: 3.6 × (2 + 8) = 3.6 × 10 = 36.

Part B: Choose, or true or false

1. 9. A. 6.2 ÷ 0.8

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

   × and ÷ come before + and −: the only division is 6.2 ÷ 0.8, so it comes first.

2. 10. False

   Check the order: 1.6 × 5 comes first, then add 5.5. See whether 35.5 was worked out that way.

   Multiply first: 1.6 × 5 = 8, then 5.5 + 8 = 13.5.

3. 11. B. 8.4 ÷ 0.3

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

   × and ÷ come before + and −: the only division is 8.4 ÷ 0.3, so it comes first.

4. 12. True

   Check the order: 2.6 × 2 comes first, then add 8. See whether 13.2 was worked out that way.

   Multiply first: 2.6 × 2 = 5.2, then 8 + 5.2 = 13.2.

Part C: Word problems

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

1. 13. 1.6 m

   First find what's left after the cut, 8.3 − 3.5, then share it among 3.

   (8.3 − 3.5) ÷ 3 = 4.8 ÷ 3 = 1.6.

2. 14. 0.1 dollars

   Find what each kind costs first, 5 × 13.5 and 4 × 8.1, then add them.

   Tsz-ching paid $100, so the change is 100 minus the total.

   5 × 13.5 = 67.5 and 4 × 8.1 = 32.4, 99.9 in all; 100 − 99.9 = 0.1.

3. 15. 2 dollars

   How much does one box save? Work out 6 × 4.5 and compare it with $26.

   One by one: 2 × 6 × 4.5 = 54; boxes: 2 × 26 = 52; 54 − 52 = 2.

4. 16. 55 dollars

   How many hours are left after the first one? Each hour has two half hours, so count the half hours first.

   After the first hour come 6 half hours: 13 + 7 × 6 = 13 + 42 = 55.

5. 17. 1 L

   First find how much was poured: 5 cups of 0.3 L each, so 0.3 × 5.

   Multiply, then subtract: 2.5 − 0.3 × 5 = 2.5 − 1.5 = 1.

6. 18. 2 L

   First find how much was poured: 2 cups of 0.25 L each, so 0.25 × 2.

   Multiply, then subtract: 2.5 − 0.25 × 2 = 2.5 − 0.5 = 2.