How to Multiply Two Rational Numbers: Step-by-Step Guide

[{"selector":"#anim-084b2f74-dbec-4c24-88a7-8ee2e456711a","keyframes":{"opacity":[0,1]},"delay":200,"duration":2000,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-209a0a8f-faf6-4f5b-ac87-067e36a3c2f8","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-3fa31e14-b6e0-4008-9870-1338560e9648","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] BY Team Aakash Byju's Green Leaf Banner

A number that can be expressed as p/q, where p and q are integers and q≠0 is called a rational number.

[{"selector":"#anim-2268ba9f-3cc6-40b2-bded-5a3ea7aa5d24","keyframes":{"opacity":[0,1]},"delay":0,"duration":600,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-e2e4ccdf-e9f7-4261-ac7e-d785af42899d","keyframes":{"transform":["translate3d(-114.81482%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":600,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-dafe8488-737b-41ff-a542-7a1781130574","keyframes":{"transform":["translate3d(-115.18988%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-fd1cbc3e-eca3-4d4d-8fea-ee525373de1e","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-d1bab548-e25b-45d0-beb8-06ae53a4ce8c","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}] [{"selector":"#anim-b366acab-8423-409d-a673-259dba39e998","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-5b16a97f-fa94-438d-8bd4-768831610f43","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}]

Click Here To Attend Free Trail Class

[{"selector":"#anim-c7e454cd-0335-4a80-8c65-570a154d49bf","keyframes":[{"offset":0,"transform":"translate3d(0, -707.778%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.29,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.45,"transform":"translate3d(0, -199.0271736%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.61,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.71,"transform":"translate3d(0, -67.6635768%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.8,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.85,"transform":"translate3d(0, -25.409230200000003%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.92,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.96,"transform":"translate3d(0, -11.0413368%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":1,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"}],"delay":0,"duration":1300,"fill":"both"}] Download Aakash App

The set of rational numbers is represented by the letter "Q."

[{"selector":"#anim-db48ad35-674d-4ccf-b3e9-b52d3a4a0b63","keyframes":{"opacity":[0,1]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-f39a4f65-761a-4df4-acb7-d628b5250aee","keyframes":{"transform":["translate3d(115.65496%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-a1dc11e8-9c36-4401-9d9c-f4ce0075e361","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-12118dbd-1679-4812-8fda-586e412878d8","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}]

Multiplication of Two Rational Numbers

[{"selector":"#anim-1fe030d7-96be-434a-91d4-487f3f383946","keyframes":{"opacity":[0,1]},"delay":200,"duration":2000,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-6616f524-7140-4b5f-ba8f-3dda4452e2da","keyframes":{"opacity":[0,1]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-7699373f-08c6-4d79-ae4f-e93f174efa9f","keyframes":{"transform":["translate3d(0px, 170.01912%, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

Step 2: Multiply the Denominators and write their product as the Denominator.

[{"selector":"#anim-a7a2b11f-bdee-4c7c-8f5b-93dfeae2ab7d","keyframes":{"opacity":[0,1]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2cc076b6-1f91-4259-8900-b17bf2147699","keyframes":{"transform":["translate3d(115.65496%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-867fe303-8887-450a-aa9c-f57b1f9eb42f","keyframes":{"opacity":[0,1]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-69e6aeb8-3fd2-43e7-8bcf-6c406b109d75","keyframes":{"transform":["translate3d(-115.97444%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

Examples

[{"selector":"#anim-b90dc3b4-cca7-42ac-831c-ddd5ddb5c1bb","keyframes":{"opacity":[0,1]},"delay":200,"duration":2000,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}]

Multiplication of a rational number by zero:

[{"selector":"#anim-c0b3b05e-f983-4cfa-901b-fa0bebfa89d3","keyframes":{"transform":["rotate(10deg) translate3d(-90.36145%, 0px, 0) rotate(-10deg)","rotate(10deg) translate3d(0px, 0px, 0) rotate(-10deg)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-976c63af-f237-402f-b6a5-21a3d6b1d4cc","keyframes":{"opacity":[0,1]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b3e98670-7b7a-48fd-b15b-f94c96d88091","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}] [{"selector":"#anim-1d9e9c7a-ff74-4063-9f76-d291104eaf20","keyframes":{"transform":["rotate(-10deg) translate3d(84.16523%, 0px, 0) rotate(10deg)","rotate(-10deg) translate3d(0px, 0px, 0) rotate(10deg)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-359493a7-e4e0-473f-ac2a-5c1450c6b1c4","keyframes":{"opacity":[0,1]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2106e766-0a11-43d4-869e-cf07c745832e","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}] [{"selector":"#anim-47e67e23-af05-4352-be31-b55aed3b64d2","keyframes":{"opacity":[0,1]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-1275ce37-89a7-41f4-8f5a-fe4476ba5a32","keyframes":{"transform":["translate3d(-115.2381%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-6d60f2f2-4812-4ab0-92ef-11c974403a4e","keyframes":{"opacity":[0,1]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-117394a7-7a79-42a0-a275-3b683ccb7e5e","keyframes":{"transform":["translate3d(115.55555%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

Example of a multiplication of rational number by zero:

[{"selector":"#anim-53118787-3be7-4406-ab5c-b41082b15484","keyframes":{"transform":["rotate(10deg) translate3d(-90.36145%, 0px, 0) rotate(-10deg)","rotate(10deg) translate3d(0px, 0px, 0) rotate(-10deg)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b379b89d-9daa-4978-865f-71a32d23bc8b","keyframes":{"opacity":[0,1]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-365ef8f6-01d0-4d00-96b0-97bf2007c42c","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}] [{"selector":"#anim-8560a5e9-0329-4022-8a00-837bd735e28d","keyframes":{"transform":["rotate(-10deg) translate3d(84.16523%, 0px, 0) rotate(10deg)","rotate(-10deg) translate3d(0px, 0px, 0) rotate(10deg)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-6165eb60-8fd5-43b6-add8-d86eaacb165e","keyframes":{"opacity":[0,1]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-452b617d-5c97-4ba4-9088-33faa5eaa2f5","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}] [{"selector":"#anim-bb2416ab-6ec7-4779-a15a-984923ee8402","keyframes":{"opacity":[0,1]},"delay":200,"duration":2000,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}]

Here's how to change the sign of the product:

[{"selector":"#anim-33162984-bc0b-4c99-af1d-4a8ef316298c","keyframes":{"transform":["rotate(10deg) translate3d(-90.36145%, 0px, 0) rotate(-10deg)","rotate(10deg) translate3d(0px, 0px, 0) rotate(-10deg)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2fc31b35-8aa0-45d5-ace8-35612f36841f","keyframes":{"opacity":[0,1]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-7815d0f6-75f0-4cb9-915e-829afc8544a4","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}] [{"selector":"#anim-8bd3b7c1-6bb1-4398-ab34-4f36133447a1","keyframes":{"transform":["rotate(-10deg) translate3d(78.65749%, 0px, 0) rotate(10deg)","rotate(-10deg) translate3d(0px, 0px, 0) rotate(10deg)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-971bb6fc-050d-4142-bef2-8941fdb3a7c5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-ffa463e3-8427-4fcc-a0f1-ea160149fc48","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1600,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}] [{"selector":"#anim-f09782a5-8dad-418a-b80d-5127bc5fa323","keyframes":{"opacity":[0,1]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-76dcf7ce-6196-40d2-9e7f-7f935ecfd80b","keyframes":{"transform":["translate3d(-120.95238%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1000,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-c1e8d2e2-ac76-4235-b24e-6d3e343b5651","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-7a1de56a-9020-473e-b6b6-175223833109","keyframes":{"opacity":[0,1]},"delay":200,"duration":2000,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-a38a22bf-44cf-46e0-b2e8-d907cbcbcb35","keyframes":{"opacity":[0,1]},"delay":400,"duration":1200,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}]

How to Multiply Two Rational Numbers: Step-by-Step Guide

A number that can be expressed as p/q, where p and q are integers and q≠0 is called a rational number.

Rational Numbers

Click Here To Attend Free Trail Class

The set of rational numbers is represented by the letter "Q."

Multiplication of Two Rational Numbers

We need to follow the following steps to multiply a rational number by another rational number.

Step 2: Multiply the Denominators and write their product as the Denominator.

Step 1: Multiply the Numerators of both Numbers and write their product as the Numerator.

Examples

Multiplication of a rational number by zero:

If you multiply any rational number by zero, the result is zero.

Example of a multiplication of rational number by zero:

Here's how to change the sign of the product:

Like signs: Negative x Negative = Positive Positive x Positive = Positive Unlike signs: Positive x Negative = Negative.