Shelley wove three rugs with Seminole designs. She wrote this expression to show the total length of all three rugs she wove.
(8 7/16 + 11 9/10 ) + 15 1/10
Which shows another way to write the expression , using the Associative Property of Addition?
8 7/16 + (11 9/10 + 15 1/10)
The Associative Property of Addition states that the grouping of numbers being added does not affect the sum. In other words, you can rearrange the numbers within an addition expression and still get the same result.
To rewrite the given expression using the Associative Property of Addition, we need to group the numbers differently.
Let's first add the first two numbers, 8 7/16 and 11 9/10:
8 7/16 + 11 9/10 = 19 1/16 + 26/10
Next, we can add this sum with the third number, 15 1/10:
(19 1/16 + 26/10) + 15 1/10
Now, it's important to convert all the mixed numbers to improper fractions to ease the addition:
(305/16 + 26/10) + 151/10
To simplify the addition, we need to find a common denominator for the fractions. The least common multiple (LCM) of 16 and 10 is 80:
(305/16 * 5/5 + 26/10 * 8/8) + 151/10
Now, we can calculate:
(1525/80 + 208/80) + 151/10
Adding the fractions within each pair of parentheses:
(1733/80) + 151/10
To add the fractions with different denominators, we need to find a common denominator, which is 80:
(1733/80) + (151/10 * 8/8)
Converting the second fraction:
(1733/80) + (1208/80)
Now, we have the same denominator, so we add the numerators:
2941/80
Therefore, another way to write the expression, using the Associative Property of Addition, is:
(8 7/16 + 11 9/10) + 15 1/10 = 2941/80