Fractions in Tenths
Fractions in tenths connect decimal notation to fractional parts in Grade 8 math (Yoshiwara Core Math). One-tenth (1/10 = 0.1) is the base — if you know 1/10 of a number, you can find 2/10, 3/10, and so on. For example, 4/10 (= 0.4) of 3200 equals 3200 × 0.4 = 1280. The word 'of' signals multiplication. Tenths also appear in reverse: if 2400 is 0.6 of an amount, divide 2400 ÷ 0.6 to find the whole (4000). Understanding tenths builds fluency with decimals, percents, and proportional reasoning.
Key Concepts
Property If you can find one tenth of an amount, you can find two tenths, or three tenths, and so on. Remember that $\frac{2}{10}$ can also be written as 0.2, $\frac{3}{10}$ as 0.3, and so on. To find a fraction like $\frac{4}{10}$ (or $0.4$) of a number, first find $\frac{1}{10}$ of the number by dividing by 10, then multiply the result by 4.
Examples To find $0.7$ of 420, first find one tenth: $420 \div 10 = 42$. Then multiply by 7: $42 \times 7 = 294$. A park is 90 acres. If $0.3$ of it is woodland, the woodland area is found by first getting $\frac{1}{10}$ of 90, which is 9. Then, $9 \times 3 = 27$ acres. Out of 1500 voters, $0.6$ voted for Candidate A. First, $\frac{1}{10}$ is $1500 \div 10 = 150$. So, $150 \times 6 = 900$ people voted for Candidate A.
Explanation This is a two step move! First, find the size of one tenth by dividing. Then, multiply to get the number of tenths you need. It's like grabbing multiple slices of a pizza after you know the size of one slice.
Common Questions
How do you find 4/10 of a number?
Multiply by 0.4 (since 4/10 = 0.4). For example, 4/10 of 3200 = 3200 × 0.4 = 1280.
How do you find the whole when you know a tenth-fraction part?
Divide the known part by the decimal fraction. If 2400 is 0.6 of the total: 2400 ÷ 0.6 = 4000.
What is 3/10 as a decimal?
3/10 = 0.3.
How does knowing 1/10 help find other tenths?
Once you know 1/10 of a number, multiply that result by any digit: 3/10 of 50 = 3 × 5 = 15.
How does 'of' signal multiplication in fraction problems?
'Of' always means multiply: '0.4 of 3200' = 0.4 × 3200 = 1280.