Write three equivalent fractions to each fraction below. 5_ 3 5 11 10
The Correct Answer and Explanation is:
To find equivalent fractions for any given fraction, you multiply both the numerator and the denominator by the same non-zero number. This ensures the value of the fraction remains the same while changing its appearance. Let’s find three equivalent fractions for each of the given fractions.
Fraction 1: 53\frac{5}{3}35
To find equivalent fractions:
- Multiply both the numerator and denominator by 2:
5×23×2=106\frac{5 \times 2}{3 \times 2} = \frac{10}{6}3×25×2=610 - Multiply both the numerator and denominator by 3:
5×33×3=159\frac{5 \times 3}{3 \times 3} = \frac{15}{9}3×35×3=915 - Multiply both the numerator and denominator by 4:
5×43×4=2012\frac{5 \times 4}{3 \times 4} = \frac{20}{12}3×45×4=1220
So, the three equivalent fractions to 53\frac{5}{3}35 are:
- 106\frac{10}{6}610
- 159\frac{15}{9}915
- 2012\frac{20}{12}1220
Fraction 2: 511\frac{5}{11}115
To find equivalent fractions:
- Multiply both the numerator and denominator by 2:
5×211×2=1022\frac{5 \times 2}{11 \times 2} = \frac{10}{22}11×25×2=2210 - Multiply both the numerator and denominator by 3:
5×311×3=1533\frac{5 \times 3}{11 \times 3} = \frac{15}{33}11×35×3=3315 - Multiply both the numerator and denominator by 4:
5×411×4=2044\frac{5 \times 4}{11 \times 4} = \frac{20}{44}11×45×4=4420
So, the three equivalent fractions to 511\frac{5}{11}115 are:
- 1022\frac{10}{22}2210
- 1533\frac{15}{33}3315
- 2044\frac{20}{44}4420
Fraction 3: 103\frac{10}{3}310
To find equivalent fractions:
- Multiply both the numerator and denominator by 2:
10×23×2=206\frac{10 \times 2}{3 \times 2} = \frac{20}{6}3×210×2=620 - Multiply both the numerator and denominator by 3:
10×33×3=309\frac{10 \times 3}{3 \times 3} = \frac{30}{9}3×310×3=930 - Multiply both the numerator and denominator by 4:
10×43×4=4012\frac{10 \times 4}{3 \times 4} = \frac{40}{12}3×410×4=1240
So, the three equivalent fractions to 103\frac{10}{3}310 are:
- 206\frac{20}{6}620
- 309\frac{30}{9}930
- 4012\frac{40}{12}1240
General Rule:
To generate equivalent fractions, you multiply the numerator and denominator by any integer. For example, if you multiply by 5, you would get a new fraction, and the value would still be the same. The key to understanding equivalent fractions is recognizing that the ratio between the numerator and denominator remains constant. For example, 53\frac{5}{3}35 and 106\frac{10}{6}610 both represent the same quantity, even though they look different.
