6th-Grade Math Word Problems - Free Printable

Here are the step-by-step solutions for each word problem on the worksheet.

1. Average Speed Calculation
* Step 1: Identify the total distance and total time. The distance is 117 miles, and the time is 2.25 hours.
* Step 2: Use the formula for average speed: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$.
* Step 3: Divide 117 by 2.25.
* $117 \div 2.25 = 52$
* Check: $52 \times 2 = 104$. $52 \times 0.25$ (which is one-fourth of 52) is 13. $104 + 13 = 117$. The calculation is correct.

2. Ribbon Distribution
* Step 1: Identify the total amount of ribbon and the number of boxes. Total ribbon is 15 yards, and there are 20 boxes.
* Step 2: Divide the total ribbon by the number of boxes to find out how much each box gets.
* $15 \div 20$
* Step 3: Simplify the fraction $\frac{15}{20}$. Both numbers can be divided by 5.
* $15 \div 5 = 3$
* $20 \div 5 = 4$
* So, each box gets $\frac{3}{4}$ of a yard.
* Alternative: In decimals, $15 \div 20 = 0.75$ yards.

3. Jujubes Problem
* Step 1: Find out how many jujubes Jen ate first. She started with 12 and ate $\frac{1}{2}$ of them.
* $\frac{1}{2}$ of $12 = 6$.
* Remaining jujubes: $12 - 6 = 6$.
* Step 2: Find out how many jujubes Sam ate. He ate $\frac{1}{2}$ of the *remaining* jujubes.
* $\frac{1}{2}$ of $6 = 3$.
* Remaining jujubes after Sam: $6 - 3 = 3$.
* Step 3: Kyle left 8 jujubes for Kim. This part of the question seems to imply a separate group or a typo in the standard version of this riddle, but let's look at the specific question asked: "How many jujubes did Jen eat?"
* Step 4: Re-reading carefully: The question asks specifically about Jen.
* Jen ate $\frac{1}{2}$ of her 12 jujubes.
* Calculation: $12 \times 0.5 = 6$.
* The information about Sam, Kyle, and Kim is extra information designed to distract you if you only need to know what *Jen* ate. However, usually, these problems ask for the final remainder. Let's re-read the final sentence: "How many jujubes did Jen eat?"
* It strictly asks for Jen's consumption. Jen ate 6.
* *Self-Correction/Refinement:* Sometimes these questions are tricky. Did Jen eat more later? No, the text says "Jen ate 1/2... gave the rest to Sam." Her action is complete. The answer is simply what she ate initially.

4. Savings Pattern
* Step 1: Identify the pattern.
* January: \$2
* February: \$4
* March: \$8
* April: \$16
* The amount doubles every month ($2 \times 2 = 4$, $4 \times 2 = 8$, etc.).
* Step 2: List the savings for all 12 months.
1. Jan: \$2
2. Feb: \$4
3. Mar: \$8
4. Apr: \$16
5. May: \$32
6. Jun: \$64
7. Jul: \$128
8. Aug: \$256
9. Sep: \$512
10. Oct: \$1,024
11. Nov: \$2,048
12. Dec: \$4,096
* Step 3: Add all the amounts together to find the total.
* $2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096$
* This is a geometric series sum. Formula: $S_n = a(r^n - 1) / (r - 1)$
* $a = 2$, $r = 2$, $n = 12$
* $Sum = 2(2^{12} - 1) / (2 - 1)$
* $2^{12} = 4096$
* $Sum = 2(4096 - 1) / 1$
* $Sum = 2(4095)$
* $Sum = 8190$
* Check by adding manually:
* $2+4=6$
* $6+8=14$
* $14+16=30$
* $30+32=62$
* $62+64=126$
* $126+128=254$
* $254+256=510$
* $510+512=1022$
* $1022+1024=2046$
* $2046+2048=4094$
* $4094+4096=8190$

5. Staircase Cubes
* Step 1: Analyze the pattern in the image.
* A 3-step staircase uses 6 cubes. Let's break down why:
* Top step: 1 cube
* Middle step: 2 cubes
* Bottom step: 3 cubes
* Total: $1 + 2 + 3 = 6$. This matches the problem statement.
* Step 2: Apply the pattern to an 11-step staircase.
* We need to add the numbers from 1 to 11.
* $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11$
* Step 3: Calculate the sum.
* Using the summation formula $\frac{n(n+1)}{2}$ where $n=11$:
* $\frac{11(11+1)}{2} = \frac{11 \times 12}{2}$
* $\frac{132}{2} = 66$
* Alternatively, pair them up: $(1+11)=12, (2+10)=12, (3+9)=12, (4+8)=12, (5+7)=12$. That is five pairs of 12, plus the middle number 6.
* $5 \times 12 = 60$.
* $60 + 6 = 66$.

6. Pizza Fraction
* Step 1: Identify the starting amount. Jeff has $\frac{1}{2}$ of a pizza.
* Step 2: Identify what he eats. He eats $\frac{1}{3}$ of it (meaning $\frac{1}{3}$ of the half he has).
* Step 3: Calculate how much he ate.
* $\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$ of the original pizza.
* Step 4: Calculate what is left.
* Start with $\frac{1}{2}$ and subtract what was eaten ($\frac{1}{6}$).
* To subtract, find a common denominator. The common denominator for 2 and 6 is 6.
* Convert $\frac{1}{2}$ to sixths: $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
* Subtract: $\frac{3}{6} - \frac{1}{6} = \frac{2}{6}$.
* Step 5: Simplify the result.
* $\frac{2}{6}$ simplifies to $\frac{1}{3}$.
* Alternative Logic: If he eats $\frac{1}{3}$ of the remaining half, then $\frac{2}{3}$ of that half is left.
* $\frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3}$.

Final Answer:
1. 52 mph
2. 3/4 yard (or 0.75 yards)
3. 6 jujubes
4. $8,190
5. 66 cubes
6. 1/3