Week 22 · Comparing and adding decimals and fractions · 3 lessons
3
Adding tenths and hundredths
Discover Mathematics P4: Term 2, Unit 10, Lessons 9–12
GoalAdd tenths and hundredths by renaming the tenths as hundredths first.
New words
like denominators · the same number below the line in both fractions; fractions can be added only when they matchsum · the answer of an additionalign · to line up the decimal points one under the other
Explanation
We can add fractions only when their denominators are the same. To add tenths and hundredths, rename the tenths as hundredths first. Example: 3/10 + 23/100. Rename 3/10 = 30/100. Now add the numerators and keep the denominator: 30/100 + 23/100 = 53/100, which is 0.53. We never add the denominators: 3/10 + 23/100 is not 26/110. With decimals we can do the same job by aligning the decimal points and giving both numbers two places: 0.30 + 0.23 = 0.53. When the sum is 100/100 or more, it is one whole or more: 9/10 + 25/100 = 90/100 + 25/100 = 115/100 = 1 15/100 = 1.15.
Step
1. Rename
2. Add
3. Decimal
3/10 + 23/100
30/100 + 23/100
53/100
0.53
Worked examples
Salma walks 4/10 km to the bakery and then 35/100 km to school. How far does she walk? Rename 4/10 = 40/100. Then 40/100 + 35/100 = 75/100 = 0.75 km. The bar shows the first part, the second part and the unshaded rest of one whole kilometre.
Number
ones
tenths
hundredths
0.60
0
6
0
0.07
0
0
7
Sum 0.67
0
6
7
A jug has 0.6 L of juice and Aya pours in 0.07 L more. Align the points and use two places: 0.60 + 0.07 = 0.67 L. As fractions it is 6/10 + 7/100 = 60/100 + 7/100 = 67/100. The 7 goes in the hundredths place.
Number
9/10
25/100
Sum
As hundredths
90/100
25/100
115/100
As a decimal
0.90
0.25
1.15
Add 9/10 + 25/100. Rename 9/10 = 90/100. Then 90/100 + 25/100 = 115/100. That is one whole and 15 hundredths: 1 15/100 = 1.15. A sum can be greater than 1.
Class activity
Shop for a sum. On cards write 0.2, 0.5, 0.07, 0.35 and 0.8 as lengths of ribbon in metres. Pick any two cards, rename both with two places and add them. Write the sum as a fraction and as a decimal. Find the pair with the sum closest to 1 metre.
Practice
1
Add 2/10 + 15/100.
20/100 + 15/100 = 35/100 = 0.35.
2
Add 0.5 + 0.22.
0.50 + 0.22 = 0.72.
3
Add 3/10 + 4/100 and write the sum as a decimal.
30/100 + 4/100 = 34/100 = 0.34.
4
Add 7/10 + 40/100. Write the sum as a mixed number.
