Solved on Nov 11, 2023

A shipment of 9 tons of sugar is divided into equal-sized containers. If the shipment fills $4 \frac{2}{7}$ containers, find the amount of sugar one container can hold, expressed as a simplified mixed number.

STEP 1

Assumptions1. The total weight of the sugar is9 tons. The sugar fills $4 \frac{}{7}$ containers3. Each container holds an equal amount of sugar

STEP 2

First, we need to convert the mixed number $4 \frac{2}{7}$ to an improper fraction to make the calculation easier.
$4 \frac{2}{7} = \frac{4 \times7 +2}{7} = \frac{30}{7}$

STEP 3

Now, to find the amount of sugar one container can hold, we divide the total weight of the sugar by the number of containers.
$Sugar\, per\, container = \frac{Total\, weight\, of\, sugar}{Number\, of\, containers}$

STEP 4

Plug in the values for the total weight of the sugar and the number of containers to calculate the amount of sugar per container.
$Sugar\, per\, container = \frac{9\, tons}{\frac{30}{7}}$

STEP 5

To simplify the division of fractions, we multiply by the reciprocal of the divisor.
$Sugar\, per\, container =9\, tons \times \frac{7}{30}$

STEP 6

Calculate the amount of sugar per container.
$Sugar\, per\, container =9\, tons \times \frac{}{30} = \frac{63}{30}\, tons$

STEP 7

implify the fraction $\frac{63}{30}$ to its simplest form.
$Sugar\, per\, container = \frac{63}{30} = \frac{21}{10} =2 \frac{1}{10}\, tons$ Each container can hold $2 \frac{1}{10}$ tons of sugar.

Was this helpful?

A shipment of 9 tons of sugar is divided into equal-sized containers. If the shipment fills $4 \frac{2}{7}$ containers, find the amount of sugar one container can hold, expressed as a simplified mixed number.

STEP 1

Assumptions1. The total weight of the sugar is9 tons. The sugar fills $4 \frac{}{7}$ containers3. Each container holds an equal amount of sugar

STEP 2

First, we need to convert the mixed number $4 \frac{2}{7}$ to an improper fraction to make the calculation easier.
$4 \frac{2}{7} = \frac{4 \times7 +2}{7} = \frac{30}{7}$

STEP 3

Now, to find the amount of sugar one container can hold, we divide the total weight of the sugar by the number of containers.
$Sugar\, per\, container = \frac{Total\, weight\, of\, sugar}{Number\, of\, containers}$

STEP 4

Plug in the values for the total weight of the sugar and the number of containers to calculate the amount of sugar per container.
$Sugar\, per\, container = \frac{9\, tons}{\frac{30}{7}}$

STEP 5

To simplify the division of fractions, we multiply by the reciprocal of the divisor.
$Sugar\, per\, container =9\, tons \times \frac{7}{30}$

STEP 6

Calculate the amount of sugar per container.
$Sugar\, per\, container =9\, tons \times \frac{}{30} = \frac{63}{30}\, tons$

STEP 7

implify the fraction $\frac{63}{30}$ to its simplest form.
$Sugar\, per\, container = \frac{63}{30} = \frac{21}{10} =2 \frac{1}{10}\, tons$ Each container can hold $2 \frac{1}{10}$ tons of sugar.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

A shipment of 9 tons of sugar is divided into equal-sized containers. If the shipment fills 4274 \frac{2}{7}472​ containers, find the amount of sugar one container can hold, expressed as a simplified mixed number.

STEP 1

Assumptions1. The total weight of the sugar is9 tons. The sugar fills 474 \frac{}{7}47​ containers3. Each container holds an equal amount of sugar

STEP 2

First, we need to convert the mixed number 4274 \frac{2}{7}472​ to an improper fraction to make the calculation easier.427=4×7+27=3074 \frac{2}{7} = \frac{4 \times7 +2}{7} = \frac{30}{7}472​=74×7+2​=730​

STEP 3

STEP 4

Plug in the values for the total weight of the sugar and the number of containers to calculate the amount of sugar per container.Sugar per container=9 tons307Sugar\, per\, container = \frac{9\, tons}{\frac{30}{7}}Sugarpercontainer=730​9tons​

STEP 5

To simplify the division of fractions, we multiply by the reciprocal of the divisor.Sugar per container=9 tons×730Sugar\, per\, container =9\, tons \times \frac{7}{30}Sugarpercontainer=9tons×307​

STEP 6

Calculate the amount of sugar per container.Sugar per container=9 tons×30=6330 tonsSugar\, per\, container =9\, tons \times \frac{}{30} = \frac{63}{30}\, tonsSugarpercontainer=9tons×30​=3063​tons

STEP 7

implify the fraction 6330\frac{63}{30}3063​ to its simplest form.Sugar per container=6330=2110=2110 tonsSugar\, per\, container = \frac{63}{30} = \frac{21}{10} =2 \frac{1}{10}\, tonsSugarpercontainer=3063​=1021​=2101​tonsEach container can hold 21102 \frac{1}{10}2101​ tons of sugar.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

A shipment of 9 tons of sugar is divided into equal-sized containers. If the shipment fills $4 \frac{2}{7}$ containers, find the amount of sugar one container can hold, expressed as a simplified mixed number.

Assumptions1. The total weight of the sugar is9 tons. The sugar fills $4 \frac{}{7}$ containers3. Each container holds an equal amount of sugar

First, we need to convert the mixed number $4 \frac{2}{7}$ to an improper fraction to make the calculation easier.
$4 \frac{2}{7} = \frac{4 \times7 +2}{7} = \frac{30}{7}$

Plug in the values for the total weight of the sugar and the number of containers to calculate the amount of sugar per container.
$Sugar\, per\, container = \frac{9\, tons}{\frac{30}{7}}$

To simplify the division of fractions, we multiply by the reciprocal of the divisor.
$Sugar\, per\, container =9\, tons \times \frac{7}{30}$

Calculate the amount of sugar per container.
$Sugar\, per\, container =9\, tons \times \frac{}{30} = \frac{63}{30}\, tons$

implify the fraction $\frac{63}{30}$ to its simplest form.
$Sugar\, per\, container = \frac{63}{30} = \frac{21}{10} =2 \frac{1}{10}\, tons$ Each container can hold $2 \frac{1}{10}$ tons of sugar.