Select the three expressions that are equivalent to 5 3/4 – 2 1/4.
5 + 3/4 – (2 + 1/4)
12/4 – 1/4
23/4 – 9/4
(1 + 1 + 1 + 1 + 3/4) – (2 + 1/4)
Equivalent Expressions for 5 3/4 – 2 1/4
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Select the three expressions that are equivalent to 5 3/4 – 2 1/4.
5 + 3/4 – (2 + 1/4)
12/4 – 1/4
23/4 – 9/4
(1 + 1 + 1 + 1 + 3/4) – (2 + 1/4)
To find the expressions equivalent to (5 frac{3}{4} – 2 frac{1}{4}), we first need to convert the mixed numbers into improper fractions for easier calculation:
1. Convert to improper fractions:
– (5 frac{3}{4} = frac{5 times 4 + 3}{4} = frac{20 + 3}{4} = frac{23}{4})
– (2 frac{1}{4} = frac{2 times 4 + 1}{4} = frac{8 + 1}{4} = frac{9}{4})
Now we can rewrite the original expression:
[
5 frac{3}{4} – 2 frac{1}{4} = frac{23}{4} – frac{9}{4} = frac{23 – 9}{4} = frac{14}{4} = frac{7}{2}
]
2. Evaluate each expression for equivalence:
– Expression 1: (5 + frac{3}{4} – (2 + frac{1}{4}))
[
= 5 + frac{3}{4} – 2 – frac{1}{4} = 3 + frac{3 – 1}{4} = 3 +