Question

10
nso.2.3
solve real-world problems with positive multi-digit decimals or fractions, involving:
two steps, with addition, subtraction, and/or multiplication (l2)
a runner completed 5\frac{3}{8} miles on monday and 4\frac{1}{4} miles on tuesday.
if the runner wants to run twice the total distance on wednesday, how many miles will that be?
an art teacher gives each student 2\frac{1}{3} pounds of clay and 1\frac{1}{4} pounds of glaze for an art project.
if there are 6 students, how many pounds of materials will the teacher need?
11
nso.2.3
solve real-world problems with positive multi-digit decimals or fractions, involving:
two steps, with addition, subtraction, and/or multiplication (l2)
four friends went out to lunch and ordered the following meals:
salad: $8.75
sandwich: $12.40
pasta: $10.85
dessert: $6.95
they also shared a drink that cost $4.60. if they split the bill equally, how much does each person pay?
a scientist measured the growth of a plant over five days:
2.75 cm
3.10 cm
2.95 cm
3.05 cm
2.8 cm
if the growth is spread evenly over 5 days, how much growth happened each day?

Explanation:

First Problem (Runner's Distance):

Step1: Find total distance on Mon & Tue

Convert mixed numbers to improper fractions: \( 5\frac{3}{8}=\frac{43}{8} \), \( 4\frac{1}{4}=\frac{17}{4}=\frac{34}{8} \).
Add: \( \frac{43}{8}+\frac{34}{8}=\frac{77}{8} \) miles.

Step2: Find twice the total distance

Multiply by 2: \( 2\times\frac{77}{8}=\frac{77}{4}=19\frac{1}{4} \) miles.

Step1: Find materials per student

Add clay and glaze: \( 2\frac{1}{3}+1\frac{1}{4}=\frac{7}{3}+\frac{5}{4}=\frac{28}{12}+\frac{15}{12}=\frac{43}{12} \) pounds per student.

Step2: Find total for 6 students

Multiply by 6: \( 6\times\frac{43}{12}=\frac{43}{2}=21\frac{1}{2} \) pounds.

Step1: Find total bill

Add meal costs: \( 8.75 + 12.40 + 10.85 + 6.95 + 4.60 \).
Calculate: \( 8.75+12.40=21.15 \); \( 21.15+10.85=32 \); \( 32+6.95=38.95 \); \( 38.95+4.60=43.55 \) dollars.

Step2: Split among 4 friends

Divide by 4: \( 43.55\div4 = 10.8875 \approx 10.89 \) dollars (or exact: \( \frac{43.55}{4}=10.8875 \)).

Answer:

\( 19\frac{1}{4} \) miles

Second Problem (Art Teacher's Materials):