Isabella's Mother Has A Garden With An Area Of $10 \frac{2}{3}$ Square Feet. She Plants Peas In $\frac{1}{4}$ Of The Garden.1. The Area Used For Planting Peas Is □ \square □ .Isabella's Mother Sells The Peas And Gets

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Isabella's Mother's Garden: A Math Problem

In this article, we will explore a math problem involving a garden with an area of $10 \frac{2}{3}$ square feet. Isabella's mother plants peas in $\frac{1}{4}$ of the garden, and we need to find the area used for planting peas. This problem requires us to apply our knowledge of fractions and mixed numbers to solve a real-world scenario.

The problem states that Isabella's mother has a garden with an area of $10 \frac{2}{3}$ square feet. To understand this, we need to convert the mixed number to an improper fraction. A mixed number is a combination of a whole number and a fraction. In this case, $10 \frac{2}{3}$ can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator.

1023=(10×3)+23=30+23=32310 \frac{2}{3} = \frac{(10 \times 3) + 2}{3} = \frac{30 + 2}{3} = \frac{32}{3}

So, the area of the garden is $\frac{32}{3}$ square feet.

Isabella's mother plants peas in $\frac{1}{4}$ of the garden. To find the area used for planting peas, we need to multiply the area of the garden by the fraction of the garden that is used for planting peas.

Area used for planting peas=14×323\text{Area used for planting peas} = \frac{1}{4} \times \frac{32}{3}

To multiply fractions, we multiply the numerators and the denominators separately.

Area used for planting peas=1×324×3=3212\text{Area used for planting peas} = \frac{1 \times 32}{4 \times 3} = \frac{32}{12}

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

Area used for planting peas=32÷412÷4=83\text{Area used for planting peas} = \frac{32 \div 4}{12 \div 4} = \frac{8}{3}

So, the area used for planting peas is $\frac{8}{3}$ square feet.

Isabella's mother sells the peas and gets a certain amount of money. However, the problem does not provide any information about the price of the peas or the amount of money Isabella's mother gets. Therefore, we cannot determine the amount of money Isabella's mother gets from selling the peas.

In conclusion, Isabella's mother has a garden with an area of $10 \frac{2}{3}$ square feet. She plants peas in $\frac{1}{4}$ of the garden, and the area used for planting peas is $\frac{8}{3}$ square feet. This problem requires us to apply our knowledge of fractions and mixed numbers to solve a real-world scenario.

This problem has real-world applications in agriculture and gardening. Gardeners and farmers need to calculate the area of their gardens and the amount of space needed for planting different crops. This problem demonstrates how to apply mathematical concepts to real-world scenarios.

When solving problems involving fractions and mixed numbers, it is essential to convert mixed numbers to improper fractions. This makes it easier to perform calculations and simplify fractions.

  1. A garden has an area of $12 \frac{5}{6}$ square feet. If $\frac{1}{3}$ of the garden is used for planting flowers, what is the area used for planting flowers?
  2. A farmer has a field with an area of $20 \frac{3}{4}$ acres. If $\frac{2}{5}$ of the field is used for planting crops, what is the area used for planting crops?

  1. \frac{5}{6}$ square feet

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