Grade 4 Adding and Subtracting Decimals

What this problem type covers

Nineteen problem types across five levels: a hundred times a number given by its tenth, a place on a number line, undoing a subtraction that should have been an addition, ten times a number given as less than another, ribbon joined around a board with some left over, weighing with a box and then a rucksack, a bottle with part of its water drunk, two numbers from their sum and difference, overlapping distances along a road, a ball bouncing to a tenth of its height each time, two walkers setting off in opposite directions, the digits an inequality allows, number cards arranged closest to a target, cards arranged for the largest difference, the smallest digit a comparison allows, the largest three-place decimal under a bound, equally spaced marks on a number line, a number meeting three conditions at once, and a decimal recovered from the gap to its own digits.

Example problems

One example from each difficulty band, with worked solutions.

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1. 1 · ★1
   What number belongs in the box on the number line?
   
   • ①9
   • ②8.7
   • ③9.1
   • ④8.9
   • ⑤8.8
   Show solution

   ④8.9

   1. 8.4 to 9.4 is split into 10 equal steps, so one step is 0.1.
   2. The box is 5 steps of 0.1 on from 8.4.
   3. So the box holds 8.9.
2. 2 · ★2
   Holding a box weighing 2.21 kg, Sua weighed 33.62 kg. She put the box down, put on a rucksack, and weighed 33.33 kg. How heavy is the rucksack?
   • ①31.12 kg
   • ②31.41 kg
   • ③0.29 kg
   • ④4.13 kg
   • ⑤1.92 kg
   Show solution

   ⑤1.92 kg

   1. With the box she weighed 33.62 kg and the box is 2.21 kg, so she weighs 31.41 kg.
   2. With the rucksack she weighed 33.33 kg.
   3. So the rucksack weighs 33.33 − 31.41 = 1.92 kg.
3. 3 · ★3
   Two numbers add to 8.44 and differ by 3.94. What is 100 times the smaller one?
   • ①22.5
   • ②225
   • ③619
   • ④2.25
   • ⑤6.19
   Show solution

   ②225

   1. Adding the sum and the difference gives twice the larger number.
   2. 8.44 + 3.94 = 12.38, so the larger number is 6.19.
   3. The smaller is 8.44 − 6.19 = 2.25.
   4. 100 times 2.25 is 225.
4. 4 · ★4
   Using each of the cards 4, 6, 9, 3 once, numbers with two decimal places are made. Which one comes closest to 60?
   • ①63.49
   • ②49.63
   • ③96.43
   • ④34.69
   • ⑤96.34
   Show solution

   ①63.49

   1. The closest one below 60 is 49.63, which is 10.37 away.
   2. The closest one above 60 is 63.49, which is 3.49 away.
   3. Comparing the two gaps, 63.49 is closer.
5. 5 · ★5
   Taking the point out of a decimal gives a whole number, and that whole number is 6,005.34 more than the decimal. What was the decimal?
   • ①61.66
   • ②6.066
   • ③60.66
   • ④6,066
   • ⑤606.6
   Show solution

   ③60.66

   1. Taking the point out makes every digit worth 100 times as much, so the difference is 99 times the decimal.
   2. The whole number without the point is 6,066.
   3. Check: 6,066 − 60.66 = 6,005.34.
   4. So the decimal was 60.66.

Where people usually go wrong

• Moving the point one place too few when multiplying by a hundred.
• Undoing a wrong calculation once when it has to be undone twice.
• Adding only two sides of a rectangle when ribbon goes round all four.
• Comparing the two weighings directly, forgetting the box was put down.
• Taking off only the water that was drunk rather than all of it.
• Subtracting the two distances when the walkers set off in opposite directions.
• Including the boundary digit itself among the digits that fit.
• Giving the larger of the two numbers when the smaller one was asked for.