Math Problem Statement

Mary bought 9/10 m of ribbon. She used 5/6 of it to tie a present. With the remaining ribbon, she made 3 bows. How much ribbon was used to make 1 bow?

Solution

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Problem:

  • Mary bought 9/10 meters of ribbon.
  • She used 5/6 meters to tie a present.
  • With the remaining ribbon, she made 3 bows.
  • We need to find how much ribbon was used to make 1 bow.

Solution:

  1. Step 1: Find the remaining ribbon after tying the present
    Total ribbon Mary started with: 910\frac{9}{10} meters.
    Ribbon used to tie the present: 56\frac{5}{6} meters.

    To find the remaining ribbon: Remaining ribbon=91056\text{Remaining ribbon} = \frac{9}{10} - \frac{5}{6}

    To subtract, find a common denominator for 1010 and 66:
    Least common multiple (LCM) = 3030.

    Convert the fractions: 910=2730,56=2530\frac{9}{10} = \frac{27}{30}, \quad \frac{5}{6} = \frac{25}{30}

    Subtract: 27302530=230=115\frac{27}{30} - \frac{25}{30} = \frac{2}{30} = \frac{1}{15}

    Remaining ribbon = 115\frac{1}{15} meters.


  1. Step 2: Find ribbon used for 1 bow
    The remaining ribbon is used to make 3 bows.
    Ribbon per bow: Ribbon per bow=Remaining ribbonNumber of bows=1153\text{Ribbon per bow} = \frac{\text{Remaining ribbon}}{\text{Number of bows}} = \frac{\frac{1}{15}}{3}

    Divide 115\frac{1}{15} by 33 (or multiply by 13\frac{1}{3}): 115×13=145\frac{1}{15} \times \frac{1}{3} = \frac{1}{45}

    Ribbon used for 1 bow = 145\frac{1}{45} meters.


Final Answer:

The ribbon used for 1 bow is 145\frac{1}{45} meters.


Would you like a detailed breakdown of any specific step?
Here are 5 related questions to explore further:

  1. How do you calculate the least common multiple (LCM) of two numbers?
  2. What are the steps to simplify fractions like 230\frac{2}{30} to 115\frac{1}{15}?
  3. How can you divide fractions like 115÷3\frac{1}{15} \div 3?
  4. How is subtraction of fractions applied in everyday contexts?
  5. Why is finding common denominators essential in fraction operations?

Tip: When working with fractions, always check for simplification to make results clearer.

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Math Problem Analysis

Mathematical Concepts

Fraction Operations
Subtraction of Fractions
Division of Fractions

Formulas

Remaining ribbon = Total ribbon - Ribbon used
Ribbon per bow = Remaining ribbon / Number of bows

Theorems

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Suitable Grade Level

Grade 6