Mera painted equal sections of her bedroom
wall to make a pattern. She painted
2
5
of the
wall white and
1
2
of the wall lavender. Write
an equivalent fraction for each fraction using
a common denominator.
2/5 = 4/10
1/2 = 5/10
To find a common denominator for 5 and 2, we can multiply them together. Therefore, the common denominator is 10.
To express 2/5 with a denominator of 10, we need to multiply the numerator and denominator by 2:
2/5 = (2*2)/(5*2) = 4/10
To express 1/2 with a denominator of 10, we need to multiply the numerator and denominator by 5:
1/2 = (1*5)/(2*5) = 5/10
Therefore, the equivalent fractions for 2/5 and 1/2 using a common denominator of 10 are 4/10 and 5/10, respectively.
To write equivalent fractions with a common denominator, you need to find the least common multiple (LCM) of the denominators and then multiply both the numerator and denominator by the appropriate factor.
The denominators in the given fractions are 5 and 2. To find the LCM, let's list the multiples of both denominators and find their common multiple:
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, ...
From the list of multiples, we can see that 10 is the smallest common multiple of both 5 and 2.
Now, let's calculate the equivalent fractions using the common denominator of 10:
For the fraction 2/5:
Multiply the numerator by 2 (since 5 * 2 = 10) and multiply the denominator by 2 as well:
2/5 = (2 * 2) / (5 * 2) = 4/10
For the fraction 1/2:
Multiply the numerator by 5 (since 2 * 5 = 10) and multiply the denominator by 5 as well:
1/2 = (1 * 5) / (2 * 5) = 5/10
Therefore, the equivalent fractions with a common denominator of 10 are 4/10 and 5/10.