Let's assume the rational number we need to divide -25/49 by is x.
So, we have:
(-25/49) ÷ x = -5/7
Multiplying both sides by x, we get:
-25/49 = (-5/7) * x
Multiplying both sides by -49/25, we get:
(-49/25) * (-25/49) = (-49/25) * (-5/7) * x
Simplifying, we get:
1 = (7/5) * x
Therefore, x = 5/7 * 1/7 = 5/49.
So, -25/49 divided by 5/49 gives us -5/7.
Answer:
[tex]\boxed{\bf \: - \dfrac{25}{49} \: is \: divided \: by \: \dfrac{5}{7} \: to \: get \: \bigg( - \dfrac{5}{7} \bigg) \: } \\ [/tex]
Step-by-step explanation:
We have to find by what rational number should - 25/49 be divided to get - 5/7.
Let assume that required rational number be x by which - 25/49 be divided to get - 5/7.
So,
[tex]\sf \: \bigg( - \dfrac{25}{49} \bigg) \div x = \bigg( - \dfrac{5}{7} \bigg) \\ [/tex]
[tex]\sf \:x = \bigg( - \dfrac{25}{49} \bigg) \div \bigg( - \dfrac{5}{7} \bigg) \\ [/tex]
[tex]\sf \:x = \dfrac{25}{49} \div \dfrac{5}{7} \\ [/tex]
[tex]\sf \:x = \dfrac{25}{49} \times \dfrac{7}{5} \\ [/tex]
[tex]\implies\sf \: x = \dfrac{5}{7} \\ [/tex]
Hence,
[tex]\implies\sf \:\boxed{\bf \: - \dfrac{25}{49} \: is \: divided \: by \: \dfrac{5}{7} \: to \: get \: \bigg( - \dfrac{5}{7} \bigg) \: } \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
1. Commutative Property of Addition.
[tex]\sf \: \boxed{ \sf{ \:a + b = b + a \: }} \\ [/tex]
2. Associative Property of Addition
[tex]\sf \: \boxed{ \sf{ \:(a + b) + c = a + (b + c) \: }} \\[/tex]
3. Additive Identity
[tex]\sf \: \boxed{ \sf{ \:x + 0 = 0 + x = x \: }} \\ [/tex]
4. Commutative Property of Multiplication
[tex]\sf \: \boxed{ \sf{ \:a \times b = b \times a \: }} \\ [/tex]
5. Associative Property of Multiplication
[tex]\sf \: \boxed{ \sf{ \:(a \times b) \times c = a \times (b \times c) \: }} \\[/tex]
6. Multiplicative Identity
[tex]\sf \: \boxed{ \sf{ \:x \times 1 = 1 \times x = x \: }} \\ \\ [/tex]
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Answers & Comments
Let's assume the rational number we need to divide -25/49 by is x.
So, we have:
(-25/49) ÷ x = -5/7
Multiplying both sides by x, we get:
-25/49 = (-5/7) * x
Multiplying both sides by -49/25, we get:
(-49/25) * (-25/49) = (-49/25) * (-5/7) * x
Simplifying, we get:
1 = (7/5) * x
Therefore, x = 5/7 * 1/7 = 5/49.
So, -25/49 divided by 5/49 gives us -5/7.
Verified answer
Answer:
[tex]\boxed{\bf \: - \dfrac{25}{49} \: is \: divided \: by \: \dfrac{5}{7} \: to \: get \: \bigg( - \dfrac{5}{7} \bigg) \: } \\ [/tex]
Step-by-step explanation:
We have to find by what rational number should - 25/49 be divided to get - 5/7.
Let assume that required rational number be x by which - 25/49 be divided to get - 5/7.
So,
[tex]\sf \: \bigg( - \dfrac{25}{49} \bigg) \div x = \bigg( - \dfrac{5}{7} \bigg) \\ [/tex]
[tex]\sf \:x = \bigg( - \dfrac{25}{49} \bigg) \div \bigg( - \dfrac{5}{7} \bigg) \\ [/tex]
[tex]\sf \:x = \dfrac{25}{49} \div \dfrac{5}{7} \\ [/tex]
[tex]\sf \:x = \dfrac{25}{49} \times \dfrac{7}{5} \\ [/tex]
[tex]\implies\sf \: x = \dfrac{5}{7} \\ [/tex]
Hence,
[tex]\implies\sf \:\boxed{\bf \: - \dfrac{25}{49} \: is \: divided \: by \: \dfrac{5}{7} \: to \: get \: \bigg( - \dfrac{5}{7} \bigg) \: } \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
1. Commutative Property of Addition.
[tex]\sf \: \boxed{ \sf{ \:a + b = b + a \: }} \\ [/tex]
2. Associative Property of Addition
[tex]\sf \: \boxed{ \sf{ \:(a + b) + c = a + (b + c) \: }} \\[/tex]
3. Additive Identity
[tex]\sf \: \boxed{ \sf{ \:x + 0 = 0 + x = x \: }} \\ [/tex]
4. Commutative Property of Multiplication
[tex]\sf \: \boxed{ \sf{ \:a \times b = b \times a \: }} \\ [/tex]
5. Associative Property of Multiplication
[tex]\sf \: \boxed{ \sf{ \:(a \times b) \times c = a \times (b \times c) \: }} \\[/tex]
6. Multiplicative Identity
[tex]\sf \: \boxed{ \sf{ \:x \times 1 = 1 \times x = x \: }} \\ \\ [/tex]