Solve Problem with Rational Numbers
Greg bought 9 11/16 gallons of gas. What decimal should the meter on the gas pump read?
19.6875
(3 + 4 )4 - (43 + 4)3
−312,031
2401−314,432=−312,031
Step 1: Simplify inside the parentheses
Step 2: Calculate the powers
Step 3: Subtract
Find the Product:
6(-5)(3)
Step-by-step:
6×−5=−306
−30×3=−90
✅ Final Answer:
−90
Samantha has 3/4 of a yard of ribbon. She wants to cut it into pieces that are each 1/8 of a yard long. How many pieces can she make?
Step 1: Keep the first fraction, change to multiplication, flip the second:
3/4×8/1=24/4
Step 2: Simplify:
24/4=6
Samantha can cut 6 pieces of ribbon.
150
1
What is the decimal equivalent of the rational number?
-17/5
-3.4
Find the sum:
25.47+(−5.6)+4.13
Step 1:
Add 25.47 and −5.6=19.87
Step 2: Add 19.87 and 4.13
=24.00
Final Answer:
24.00
4(−7)2
✅ Final Answer:
−56
What is the value of the expression:
−2 2/5 ÷(−1.5)
Step 1: Convert the mixed number to an improper fraction
Step 2: Rewrite division as multiplication by the reciprocal
Step 3: Simplify the signs
Step 4: Multiply the fractions
Step 5: Simplify the fraction
Step 6: Convert to mixed number
✅ Final Answer:
1 3/5
Which expression is equivalent to 0.6259 / 0.6253
(0.625)6
Use the Quotient of Powers: bases are the same, subtract exponents
Rewrite the following fraction as a mixed number.
-2.45
-2 9/20
Find the sum
25.47+(−4.15)+6.38
27.70
Step 1: Add 25.47 and −4.15 = 21.32
Step 2: Add 21.32 and 6.38 =27.70
Find the product
−3(8)(−4)
✅ Final Answer:
96
What is the value of ((10−|−8|)÷3)+52
Step 1: Find the absolute value
∣−8∣=8
Step 2: Substitute the absolute value
(10−8)÷3))+52
Step 3: Simplify inside the parentheses
10−8=2
Step 4: Divide by 3
2÷3=2/3
Step 5: Calculate 52 = 25
Step 6: Add the results
2/3 + 25 =25 + 2/3= 75/3 + 2/3=77/3 ≈25.67
✅ Final Answer:
77/3 or approximately 25.67
What expression is equivalent to
42 x 75/ 74
Use the Quotient of Powers rule: same base, subtract exponents.
5-4 =1
42 x 7
In 5 rounds of a game, Jill scored -3,8,9,-7, and 13. What integer represents her average score for the 5 rounds?
-3 + 8 + 9 +-7 +13 = 20;
20 / 5 =4
Jessica had 5.75 liters of juice. She drank 2.3 liters in the morning and then gave away 1.25 liters to her friend. How many liters of juice does Jessica have left?
Total juice Jessica drank and gave away:
2.3+1.25=3.55
Juice left:
5.75−3.55= 2.20
Jessica has 2.20 liters of juice left.
What is the value of the expression
6.2+(12.6÷2)×3+10
Step 1: Divide
12.6÷2=6.3
Step 2: Multiply
6.3×3=18.9
Step 3: Add
6.2+18.9 =35.1
✅ Final Answer:
35.1
What is the value of the expression −3 1/3 ÷ (−2.4)
Step 1: Convert the mixed number to an improper fraction
Step 2: Rewrite the division as multiplication by the reciprocal
Step 3: Simplify the signs
Step 4: Multiply the fractions
Step 5: Simplify the fraction
✅ Final Answer:
1 7/18
Which expression is equivalent to (2)2 x (3)2/ (5)2+3
Numerator:
22⋅32No exponent rule combines bases 2 and 3, so leave it as is or multiply if you want (but rules don’t simplify this further).
Denominator: (5)2+3
Since it's addition, you cannot apply any exponent rule here.
You must leave it as it is or evaluate the numbers directly.
Exponent rules apply only to multiplication and division of powers with the same base, or powers raised to powers.
You cannot apply exponent rules to sums like a3+a2
Step 1: Convert the mixed number to an improper fraction 3 1/2 = 7/2
Step 2: Multiply rate × time 7/2 x 10
✅ Final Answer:
35 feet
Carlos drank 5/6 of a bottle of juice. Later, he spilled 1/4 of the bottle. How much juice is left in the bottle?
Step 1: Find a common denominator for 5/6 and 1/4.
The least common denominator is 12.
Step 2: Subtract the spilled amount from the amount he drank:
7/12
What is the value of the expression
4.5+(16.8÷4)×2+7.5
Step 1: Divide
16.8÷4=4.2
Step 2: Multiply
4.2×2=8.4
Step 3: Add everything together
4.5+8.4=20.4
✅ Final Answer:
20.4
A tank holds 4 ¾ gallons of water. Each container can hold 1 ½ gallons. How many full containers can be filled from the tank?
Step 1: Convert to improper fractions:
Step 2: Multiply by the reciprocal:
Step 3: Simplify:
✅ Final Answer:
You can fill 3 full containers, with 1/6of a gallon of water left over.
Ryan has 1.75 meters of satin ribbon. Which fraction correctly represents the length of ribbon Ryan has?
1 3/4 m