Question

1. draw a model. then, write the numerical expressions.

a. the sum of 21 and 4, doubled
b. 5 times the sum of 7 and 23
c. 2 times the difference between 49.5 and 37.5
d. the sum of 3 fifteens and 4 twos
e. the difference between 9 thirty - sevens and 8 thirty - sevens
f. triple the sum of 45 and 55

Explanation:

Step1: Analyze "The sum of 21 and 4, doubled"

First find sum: $(21 + 4)$, then double it: $2\times(21 + 4)$

Step2: Analyze "5 times the sum of 7 and 23"

Find sum first: $(7+23)$, then multiply by 5: $5\times(7 + 23)$

Step3: Analyze "2 times the difference between 49.5 and 37.5"

Find difference: $(49.5-37.5)$, then multiply by 2: $2\times(49.5 - 37.5)$

Step4: Analyze "The sum of 3 fifteens and 4 twos"

3 fifteens is $3\times15$, 4 twos is $4\times2$, sum is $(3\times15)+(4\times2)$

Step5: Analyze "The difference between 9 thirty - sevens and 8 thirty - sevens"

9 thirty - sevens is $9\times37$, 8 thirty - sevens is $8\times37$, difference is $9\times37-8\times37$

Step6: Analyze "Triple the sum of 45 and 55"

Find sum: $(45 + 55)$, then triple it: $3\times(45 + 55)$

Answer:

a. $2\times(21 + 4)$
b. $5\times(7 + 23)$
c. $2\times(49.5 - 37.5)$
d. $(3\times15)+(4\times2)$
e. $9\times37-8\times37$
f. $3\times(45 + 55)$